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Welcome to the presentation on multiplying and

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dividing negative numbers.

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Let's get started.

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I think you're going to find that multiplying and dividing

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negative numbers are a lot easier than it might

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look initially.

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You just have to remember a couple rules, and I'm going to

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teach probably in the future like I'm actually going to give

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you more intuition on why these rules work.

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But first let me just teach you the basic rules.

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So the basic rules are when you multiply two negative numbers,

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so let's say I had negative 2 times negative 2.

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First you just look at each of the numbers as if there

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was no negative sign.

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Well you say well, 2 times 2 that equals 4.

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And it turns out that if you have a negative times a

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negative, that that equals a positive.

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So let's write that first rule down.

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A negative times a negative equals a positive.

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What if it was negative 2 times positive 2?

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Well in this case, let's first of all look at the

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two numbers without signs.

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We know that 2 times 2 is 4.

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But here we have a negative times a positive 2, and it

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turns out that when you multiply a negative times a

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positive you get a negative.

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So that's another rule.

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Negative times positive is equal to negative.

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What happens if you have a positive 2 times a negative 2?

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I think you'll probably guess this one right, as you can tell

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that these two are pretty much the same thing by, I believe

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it's the transitive property -- no, no I think it's the

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communicative property.

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I have to remember that.

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But 2 times negative 2, this also equals negative 4.

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So we have the final rule that a positive times a negative

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also equals the negative.

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And actually these second two rules, they're kind

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of the same thing.

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A negative times a positive is a negative, or a positive

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times a negative is negative.

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You could also say that as when the signs are different and

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you multiply the two numbers, you get a negative number.

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And of course, you already know what happens when you have a

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positive times a positive.

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Well that's just a positive.

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So let's review.

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Negative times a negative is a positive.

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A negative times a positive is a negative.

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A positive times a negative is a negative.

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And positive times each other equals positive.

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I think that last little bit completely confused you.

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Maybe I can simplify it for you.

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What if I just told you if when you're multiplying and they're

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the same signs that gets you a positive result.

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And different signs gets you a negative result.

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So that would be either, let's say a 1 times 1 is equal to 1,

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or if I said negative 1 times negative 1 is equal to

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positive 1 as well.

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Or if I said 1 times negative 1 is equal to negative 1, or

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negative 1 times 1 is equal to negative 1.

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You see how on the bottom two problems I had two different

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signs, positive 1 and negative 1?

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And the top two problems, this one right here

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both 1s are positive.

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And this one right here both 1s are negative.

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So let's do a bunch of problems now, and hopefully it'll hit

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the point home, and you also could try to do along the

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practice problems and also give the hints and give you what

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rules to use, so that should help you as well.

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So if I said negative 4 times positive 3, well 4 times

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3 is 12, and we have a negative and a positive.

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So different signs mean negative.

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So negative 4 times 3 is a negative 12.

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That makes sense because we're essentially saying what's

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negative 4 times itself three times, so it's like negative 4

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plus negative 4 plus negative 4, which is negative 12.

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If you've seen the video on adding and subtracting negative

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numbers, you probably should watch first.

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Let's do another one.

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What if I said minus 2 times minus 7.

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And you might want to pause the video at any time to see if you

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know how to do it and then restart it to see

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what the answer is.

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Well, 2 times 7 is 14, and we have the same sign here, so

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it's a positive 14 -- normally you wouldn't have to write the

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positive but that makes it a little bit more explicit.

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And what if I had -- let me think -- 9 times negative 5.

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Well, 9 times 5 is 45.

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And once again, the signs are different so it's a negative.

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And then finally what if it I had -- let me think of some

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good numbers -- minus 6 times minus 11.

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Well, 6 times 11 is 66 and then it's a negative and

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negative, it's a positive.

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Let me give you a trick problem.

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What is 0 times negative 12?

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Well, you might say that the signs are different, but

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0 is actually neither positive nor negative.

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And 0 times anything is still 0.

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It doesn't matter if the thing you multiply it by is a

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negative number or a positive number.

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0 times anything is still 0.

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So let's see if we can apply these same rules to division.

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It actually turns out that the same rules apply.

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If I have 9 divided by negative 3.

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Well, first we say what's 9 divided by 3?

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Well that's 3.

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And they have different signs, positive 9, negative 3.

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So different signs means a negative.

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9 divided by negative 3 is equal to negative 3.

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What is minus 16 divided by 8?

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Well, once again, 16 divided by 8 is 2, but

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the signs are different.

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Negative 16 divided by positive 8, that equals negative 2.

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Remember, different signs will get you a negative result.

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What is minus 54 divided by minus 6?

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Well, 54 divided by 6 is 9.

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And since both terms, the divisor and the dividend, are

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both negative -- negative 54 and negative 6 -- it turns out

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that the answer is positive.

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Remember, same signs result in a positive quotient in this

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example we did before, it was product.

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Let's do one more.

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Obviously, 0 divided by anything is still 0.

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That's pretty straightforward.

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And of course, you can't divide anything by 0

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-- that's undefined.

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Let's do one more.

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What is -- I'm just going to think of random numbers --

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4 divided by negative 1?

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Well, 4 divided by 1 is 4, but the signs are different.

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So it's negative 4.

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I hope that helps.

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Now what I want you to do is actually try as many of these

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multiplying and dividing negative numbers as you can.

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And you click on hints and it'll remind you

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of which rule to use.

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In your own time you might want to actually think about why

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these rules apply and what it means to multiply a negative

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number times a positive number.

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And even more interesting, what it means to multiply a negative

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number times a negative number.

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But I think at this point, hopefully, you are ready to

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start doing some problems.

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Good luck.

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